Stability analysis of an autocatalytic protein model

A wide range of cellular processes require molecular regulatory pathways to convert a graded signal into a discrete response. One prevalent switching mechanism relies on the coexistence of two stable states (bistability) caused by positive feedback regulations. Intriguingly, positive feedback is often supplemented with negative feedback, raising the question of whether and how these two types of feedback can cooperate to control discrete cellular responses. To address this issue, we formulate a canonical model of a protein–protein interaction network and analyze the dynamics of a prototypical two-component circuit. The appropriate combination of negative and positive feedback loops can bring a bistable circuit close to the oscillatory regime. Notably, sharply activated negative feedback can give rise to a bistable regime wherein two stable fixed points coexist and may collide pairwise with two saddle points. This specific type of bistability is found to allow for separate and flexible control of switch-on and switch-off events, for example (i) to combine fast and reversible transitions, (ii) to enable transient switching responses and (iii) to display tunable noise-induced transition rates. Finally, we discuss the relevance of such bistable switching behavior, and the circuit topologies considered, to specific biological processes such as adaptive metabolic responses, stochastic fate decisions and cell-cycle transitions. Taken together, our results suggest an efficient mechanism by which positive and negative feedback loops cooperate to drive the flexible and multifaceted switching behaviors arising in biological systems.

Application of the least-squares inversion method: Fourier series versus waveform inversion

Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about non-perturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected. Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations. To demonstrate some of these ideas, we study the SU(N) principal chiral model (PCM), a two dimensional asymptotically free matrix field theory which has no instantons, because the relevant homotopy group is trivial. Adiabatic continuity is used to reach a weakly coupled regime where NP effects are calculable. We then use resurgence theory to uncover the existence and role of novel ‘fracton’ saddle points, which turn out to be the fractionalized constituents of previously observed unstable ‘uniton’ saddle points. The fractons play a crucial role in the physics of the PCM, and are responsible for the dynamically generated mass gap of the theory. Moreover, we show that the fracton-anti-fracton events are the weak coupling realization of ’t Hooft’s renormalons, and argue that the renormalon ambiguities are systematically cancelled in the semi-classical expansion. Our results motivate the conjecture that the semi-classical expansion of the path integral can be geometrized as a sum over Lefschetz thimbles.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2008Frquency‐domain elastic waveform inversion with irregular surface topographyAuthors: UGeun JangDong‐Joo MinYunseok ChoiChangsoo ShinUGeun JangSeoul National UniversitySearch for more papers by this author, Dong‐Joo MinSeoul National UniversitySearch for more papers by this author, Yunseok ChoiSeoul National UniversitySearch for more papers by this author, and Changsoo ShinSeoul National UniversitySearch for more papers by this authorhttps://doi.org/10.1190/1.3059291 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract In order to describe the irregular topography that is commonly encountered in land‐based seismic exploration, we present a frequency‐domain elastic wave modeling algorithm for this phenomenon, incorporated into an elastic waveform inversion algorithm. We use a finite‐element method, both for the modeling and for the inversion algorithms, in which the main body is approximated by rectangular elements and irregular topography is described by triangular elements. In common with conventional finite‐element modeling algorithms, our finiteelement irregular topography modeling algorithm also naturally satisfies the free‐surface boundary condition due to the Neumann boundary condition, which is incorporated when we construct the finite‐element formulae. For the inversion algorithm, we use the steepest‐descent method, and scale the gradient direction using the diagonal of the pseudo‐Hessian matrix rather than the approximate or full Hessian matrix. We apply the inversion technique to the AA‐line of the SEG/EAGE salt dome model, modified to account for irregular surface topography. Through numerical examples, we demonstrate that our elastic waveform inversion can reproduce subsurface structures and elastic parameters fairly well, even for a model with irregular topography.Permalink: https://doi.org/10.1190/1.3059291FiguresReferencesRelatedDetailsCited ByFrequency-domain elastic-wave modeling for polygonal topography using rotated average-derivative difference operators18 September 2020 | Acta Geophysica, Vol. 68, No. 5Frequency-Domain Finite-Difference Elastic Wave Modeling in the Presence of Surface Topography8 January 2020 | Pure and Applied Geophysics, Vol. 177, No. 6Multi-scale full waveform inversion for areas with irregular surface topography in an auxiliary coordinate system6 December 2018 | Exploration Geophysics, Vol. 49, No. 1 SEG Technical Program Expanded Abstracts 2008ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2008 Pages: 3713 publication data© 2008 Copyright © 2008 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 15 Dec 2008 CITATION INFORMATION UGeun Jang, Dong‐Joo Min, Yunseok Choi, and Changsoo Shin, (2008), "Frquency‐domain elastic waveform inversion with irregular surface topography," SEG Technical Program Expanded Abstracts : 2031-2035. https://doi.org/10.1190/1.3059291 Plain-Language Summary PDF DownloadLoading ...

Oscillation dynamics of MeKS core module containing positive and negative feedback loops with time delay

Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn4 group. The results are in excellent agreement with previously reported experimental measurements on this system.

How can cells shape and utilize dynamic gene regulation to enable complex cellular behaviors? I study this question in natural and synthetic contexts. The first project studies how a natural genetic network can imbue cells with a sense of ‘time’. It has long been known that environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable ‘polyphasic’ positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a timer that operates over time scales much longer than a cell cycle. The second project proposes a method to rapidly generate and test complex genetic network dynamics in living cells. Existing microorganisms have evolved genetic circuitry to meet diverse challenges and maximize their survival and fitness. These challenges arise from external environmental pressures, or internal evolved constraints. Furthermore, these challenges may be either static or dynamic in nature. While existing circuits have likely evolved to be ‘good enough’ to respond to historical challenges, it remains unclear if they can be improved upon, and whether they respond well to novel situations. Synthetic biology seeks to engineer organisms with complex novel phenotypes, both to harness these novel organisms for a function and to understand their underlying biology. Dynamic gene expression strategies may be necessary to successfully generate these phenotypes. Unfortunately, generating novel dynamic gene expression patterns with conventional genetic engineering remains a challenge. Here I propose and describe progress towards a computerized feedback control setup to enable the programming and rapid testing of dynamic gene regulatory patterns in living cells. Small sets of genes will be regulated optogenetically based on programmed control laws, and past and present cellular state. This setup will enable us to explore the functions and limits of engineered dynamic gene regulation, while hopefully, in the process, providing lessons about the underlying biology.

Summry— Cell signaling pathways interact with one another to form networks in mammalian systems. Such networks are complex in their organization and exhibit emergent properties such as bistability and ultrasensitivity. Analysis of signaling networks requires a combination of experimental and theoretical approaches including the development and analysis of models. This review focuses on theoretical approaches to understanding cell signaling networks. Using heterotrimeric G protein pathways an example, we demonstrate how interactions between two pathways can result in a network that contains a positive feedback loop and function as a switch. Different mathematical approaches that are currently used to model signaling networks are described, and future challenges including the need for databases as well as enhanced computing environments are discussed.

Modeling Cell Signaling Networks

Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

This research is focused on discussing the SEIQRS epidemic model for the spread of the COVID-19 disease with a nonlinear incidence rate. From the result of analysis of the SEIQR model obtained two equilibrium point these are diseases free equilibrium points and endemic equilibrium point. Then, the analysis of the completion behavior is done by using eigenvalues and stability around equilibrium point, the obtained result of the diseases free equilibrium point has two stability traits are saddle point, and stable. The stability diseases free equilibrium will be stable when R0 1, if R0 1 then the equilibrium point is not stable (saddle point) and conversely the positive endemic equilibrium point will be spiral stable. In numerical analysis, it is done by varying the parameter values and using the fourth order runge-kutta approach.

Benefits of a Testing Framework in Undergraduate C Programming Courses

In contrast to un-catalyzed hydrolysis of organophosphorus (OP) compounds, metal ions or/and their complexes with chelating ligands show catalytic effects in several ways depending upon the nature of the metal, ligand, substrate, and medium. It is known that Cu(II)-en chelate containing copper complexes accelerate the hydrolysis of OP compounds. However, the mechanism for this rate enhancement in the Cu(II)-en chelate catalytic hydrolysis reaction of sarin remains unexplored. We have examined possible mechanisms involving a Cu(II)-en with hydroxide nucleophile for the reaction pathway of the hydrolysis of O-isopropyl methylphosphonofluoridate (sarin) computationally. The density functional (B3LYP) employed in this study has reproduced the experimental Gibb’s free energy of activation value 15.5 kcal/mol for alkaline hydrolysis of sarin. Earlier proposal of push–pull mechanism for metal ion chelate-catalyzed hydrolysis of OP compounds has been found to be unfavorable in the present study. The role of water molecules in catalyzing the hydrolysis of sarin with Cu(II)-en chelate is crucial. The catalytic process involving Cu(II)-en chelate with one water molecule is the more plausible pathway to achieve the hydrolysis of sarin with Cu(II)-en chelate complexes. The most popular B3LYP method was used for optimization of given geometries. Except LANL2DZ for Cu atom, all the atoms are described using the 6–31 + G(d) basis set. The stability test has been performed for the wave functions as we are dealing with the open-shell molecules in order to ensure stable electronic configuration form, and the stable wavefunction is used as the initial configuration for the subsequent optimization. Harmonic frequency calculations and thermodynamic corrections were performed at the same level of theory. PCM method has been used for solvation effects. In order to ensure that each saddle point is linked to a minimum, IRC calculations were performed in forward and reverse directions to ensure the eigenvectors associated with the unique negative eigenvalues of the Hessian matrix. All energies discussed are solvated Gibbs free energies corrected to 298.15 K for the relative stability of the chemical structure. All calculations were performed using the Gaussian 09 code.

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory with a sign problem is derived. Although charge conjugation $\mathcal{C}$ is broken at finite density, there remains a symmetry under $\mathcal{CK}$, where $\mathcal{K}$ is complex conjugation. We consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The thermodynamic behavior is extracted from $\mathcal{CK}$-symmetric complex saddle points of the effective field theory at tree level. The relativistic and static fermions show a liquid-gas transition, manifesting as a first-order line at low temperature and high density, terminated by a critical end point. In the cases of nonrelativistic fermions and classical particles, we find no first-order liquid-gas transitions at tree level. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the $\mathcal{CK}$ symmetry of the models, the eigenvalues of the mass matrix can be complex. This leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one or two disorder lines are found. Numerical results for relativistic fermions give a very similar picture.

Mathematical analysis for stochastic model of Alzheimer’s disease